Many technical systems are constructed from modules, and data signals containing information, i.e., data, are exchanged between the modules, i.e., transferred from one module to an adjacent module. These modules do not necessarily need to be located physically close together. Because transfer channels are limited in terms of their data rate, often only reduced information is transferred from one module into an adjacent module. One example thereof is a radar system of a device for a vehicle for automatic spacing control via radar (“ACC”). A large volume of measurement data is received by this radar system, but what is derived therefrom and transferred is only a current spacing from one or more preceding vehicles, and their relative speeds. All further information, for example how good the reception conditions were, is lost. This is, however, extremely important for further processing of the signals, i.e., data, especially for an estimate as to how trustworthy the signals are. Another example is position determination by way of satellite navigation systems, or “GNSS.” Usually only a position is transferred from a GNSS module. How reliable the measurement of the position was, i.e., the quality of the reception conditions, is not evident from the position indication. This information is very important, however, for further processing of that position, e.g., for combination with other sensor signals.
In general, often only the results of a filtering operation and/or evaluation operation are available, without further information. A user often additionally requires statistical statements regarding the instantaneous, actual (i.e., real) measured data that existed as raw measured values, i.e., raw measured data, prior to the filtering operation. Variances of the measured values are often utilized for such statistical statements.
Reference will be made below to the theory of linear filters, in particular the Kalman filter theory, which relates to the filtering of raw measured values to yield a useful signal, ranging from very simple filters (e.g., low-pass filters) to Kalman filters that constitute optimum observers. The Kalman filter is a set of mathematical equations with which, when error-affected observations are present, conclusions are possible as to the state of many technical systems, as is evident from, for example, the Internet site of de.wikipedia.org/wiki/Kalman-Filter as presented in 2014. In simplified terms, the Kalman filter serves to remove interference caused by measurement devices. The mathematical structure both of an underlying dynamic system with which the measurements to be filtered are made, and of the measurement distortions, must be known.
It is known from the monograph by Fredrik Gustafson, “Adaptive Filtering and Change Detection,” John Wiley & Sons, Ltd.; copyright 2000, ISBN 0-471-49287-6, page 312, that the measurement noise can be calculated from the filter result if the entire filter configuration, and complete information regarding the filter values and their statistical characteristics, in particular the variances, are known.